Negative Binomial Autoregressive Process with Stochastic Intensity

2018 ◽  
Vol 40 (2) ◽  
pp. 225-247 ◽  
Author(s):  
Christian Gouriéroux ◽  
Yang Lu
Keyword(s):  
Negative Binomial ◽  
Autoregressive Process ◽  
Stochastic Intensity

Estimation in an Integer-Valued Autoregressive Process with Negative Binomial Marginals (NBINAR(1))

2012 ◽  
Vol 41 (4) ◽  
pp. 606-618 ◽  
Author(s):  
Miroslav M. Ristić ◽  
Aleksandar S. Nastić ◽  
Hassan S. Bakouch
Keyword(s):  
Negative Binomial ◽  
Autoregressive Process

scholarly journals Mortality and Excess Mortality: Improving FluMOMO

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Luís Portugal
Keyword(s):  
Excess Mortality ◽  
Linear Models ◽  
Negative Binomial ◽  
Heat Waves ◽  
Activity Index ◽  
Autoregressive Process ◽  
Extreme Temperatures ◽  
Linear Predictor ◽  
Risk Of Death ◽  
Influenza Activity

FluMOMO is a universal formula to forecast mortality in 27 European countries and was developed on EuroMOMO context, http://www.euromomo.eu. The model has a trigonometric baseline and considers any upwards deviation from that to come from flu or extreme temperatures. To measure it, the model considers two variables: influenza activity and extreme temperatures. With the former, the model gives the number of deaths because of flu and with the latter the number of deaths because of extreme temperatures. In this article, we show that FluMOMO lacks important variables to be an accurate measure of all-cause mortality and flu mortality. Indeed, we found, as expected, that population ageing and exposure to the risk of death cannot be excluded from the linear predictor. We model weekly deaths as an autoregressive process (lag of one together with a lead of one week). This step allowed us to avoid FluMOMO trigonometric baseline and have a fit to weekly deaths through demographic variables. Our model uses data from Portugal between 2009 and 2020, on ISO-week basis. We use negative binomial-generalized linear models to estimate the weekly number of deaths as an alternative to traditional overdispersion Poisson. As explanatory variables were found to be statistically significant, we registered the number of deaths from the previous week, the influenza activity index, the population average age, the heat waves, the flu season, the number of deaths with COVID-19, and the population exposed to the risk of dying. Considering as excess mortality the number of deaths above the best estimate of deaths from our model, we conclude that excess mortality in 2020 (net of COVID-19 deaths, heat wave of July, and ageing) is low or inexistent. The model also allows us to have the number of deaths arising from flu and we conclude that FluMOMO is overestimating deaths from flu by 78%. Averages from the probability of dying are obtained as well as the probability of dying from flu. The latter is shown to be decreasing over time, probably due to the increase of flu vaccination. Higher mortality detected with the start of COVID-19, in March-April 2020, was probably due to COVID-19 deaths not recognized as COVID-19 deaths.

A Flexible Observation-Driven Stationary Bivariate Negative Binomial INAR(1) with Non-homogeneous Levels of Over-dispersion

2017 ◽  
Vol 10 (2) ◽  
Author(s):  
Naushad Mamode Khan ◽  
Yuvraj Sunecher ◽  
Vandna Jowaheer
Keyword(s):  
Negative Binomial ◽  
Estimation Method ◽  
Autoregressive Process ◽  
Estimating Equation ◽  
Moment Condition ◽  
Dispersion Index ◽  
Unknown Parameters ◽  
Moment Conditions ◽  
Over Dispersion ◽  
Different Levels

Abstract The existing bivariate integer-valued autoregressive process of order 1 (BINAR(1)) with negative binomial (NB) innovations is developed under stationary moment conditions and in particular under same level of over-dispersion index. In this paper, we propose a flexible BINAR(1) under NB innovations where the counting series are subject to two different levels of over-dispersion under same stationary moment condition. The unknown parameters of the new model are estimated using a generalized quasi-likelihood (QL) estimating equation. The performance of this estimation method is assessed through some numerical experiments under different time dimensions.

On the generation and origin of I/f noise

1999 ◽  
Vol 4 ◽  
pp. 87-96 ◽  
Author(s):  
B. Kaulakys ◽  
T. Meškauskas
Keyword(s):  
Point Process ◽  
Solvable Model ◽  
Autoregressive Process ◽  
Wide Range ◽  
Occurrence Times

Simple analytically solvable model exhibiting 1/f spectrum in any desirably wide range of frequency is analysed. The model consists of pulses (point process) whose interevent times obey an autoregressive process with small damping. Analysis and generalizations of the model indicate to the possible origin of 1/f noise, i.e. random increments between the occurrence times of particles or pulses resulting in the clustering of the pulses.

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